The amplitude of $\frac{1 + \sqrt{3}i}{\sqrt{3} + i}$ is

If $z$ is a complex number of unit modulus and argument $\theta$,then $\text{arg}\left( \frac{1+z}{1+\bar{z}} \right)$ equals:

Let $z$ satisfy $|z| = 1$ and $z = 1 - \bar{z}$.
Statement $1$: $z$ is a real number.
Statement $2$: The principal argument of $z$ is $\frac{\pi}{3}$.

If complex numbers $z_1$ and $z_2$ are such that $|z_1| = \sqrt{2}$,$|z_2| = \sqrt{3}$ and $|z_1 + z_2| = \sqrt{5 - 2\sqrt{3}}$,then the value of $|Arg(z_1) - Arg(z_2)|$ is

If $z_1 = -\sqrt{3} + i$ and $z_2 = -\sqrt{3} - i$,then the principal amplitude of the complex number $\frac{z_1}{z_2}$ is

If $z$ is a purely real number such that $\text{Re}(z) < 0$,then $\text{arg}(z)$ is equal to